In the Proper Interval Vertex Deletion problem (PIVD), we are given a graph G and an integer parameter k > 0, and the question is whether there are at most k vertices in G whose removal results in a proper interval graph. It is known that the PIVD problem is fixedparameter tractable and admits a polynomial but “unreasonably” large kernel of O(k53) vertices. A natural question is whether the pro...

The polynomial v(x) allows us to determine the points in E(k̄) that lie in the kernel of α. Indeed, we have kerα = {(x0, y0) ∈ E(k̄) : v(x0) = 0} ∪ {0}. If E1 is defined by y 2 = f(x) = x3 + Ax + B, then we get one point in kerα for each root of v that is also a root of f (these are points (x0, 0) of order 2), two points for every other distinct root of v (since α(x0, y0) = 0 implies α(x0,−y0) = ...

This article investigates the heat kernel of two-dimensional uniform spanning tree. We improve previous work by demonstrating occurrence log-logarithmic fluctuations around leading order polynomial behaviour for on-diagonal part quenched kernel. In addition we give two-sided estimates averaged kernel, and show that exponents appear in off-diagonal parts versions differ. Finally, derive various ...

Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation order n, with convolution-type kernel. This kind extends original Hyers-Ulam whose originated 1940. A general integral formulated first, and then some particular cases (polynomial function exponential function) for from kernel are considered.

In a recent paper Soleimanfallah and Yeo proposed a kernelization algorithm for Vertex Cover which, for any xed constant c, produces a kernel of order 2k−c in polynomial time. In this paper we show how their techniques can be extended to improve the produced kernel to order 2k − c log k, for any xed constant c.

Regression analysis when the underlying regression function has jumps is a research problem with many applications. In practice, jumps often represent structure changes of a related process. Hence, it is important to detect them accurately from observed noisy data. In the literature, there are some jump detectors proposed, most of which are based on local constant or local linear kernel smoothi...

We study the error performances of p -norm Support Vector Machine classifiers based on reproducing kernel Hilbert spaces. We focus on two category problem and choose the data-dependent polynomial kernels as the Mercer kernel to improve the approximation error. We also provide the standard estimation of the sample error, and derive the explicit learning rate.

Every now and then, a new design of an interpolation kernel appears in the literature. While interesting results have emerged, the traditional design methodology proves laborious and is riddled with very large systems of linear equations that must be solved analytically. We propose to ease this burden by providing an explicit formula that can generate every possible piecewise-polynomial kernel ...

In the last few years, application of Support Vector Machines (SVMs) for solving classification and regression problems has increased, in particular, due to its high generalization performance and its ability to model non-linear relationships. The latter can only be realised if a suitable kernel function is applied. This kernel function transforms the non-linear input space into a high dimensio...

Automated inspection of apple quality involves computer recognition of good apples and blemished apples based on geometric or statistical features derived from apple images. This paper introduces a Gabor feature-based kernel principal component analysis (PCA) method by combining Gabor wavelet representation of apple images and the kernel PCA method for apple quality inspection using near-infrar...